Subgroups — C₂×C₃×C₁₇×D₂₁ #16862837

Order 4284.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₇×D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₇×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×D₂₁	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₇×C₁₇	—	3	1	no	maximal
5	C₃²×C₇×C₁₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×C₇×C₁₇	—	2	1	no	—
7	C₂×C₃×C₇×C₁₇	D₃	1	1	yes	characteristic, complemented
8	C₂×C₃×C₇×C₁₇	C₂×C₃	1	1	yes	characteristic, complemented
9	C₁₇×D₂₁	C₂×C₃	1	2	yes	direct product factor
10	C₃×D₇×C₁₇	—	3	2	no	—
11	C₂×C₃×D₃×C₁₇	—	7	1	no	maximal, Hall
12	C₂×D₇×C₁₇	—	3	1	no	Hall
13	C₃×C₇×C₁₇	—	2	1	no	—
14	C₃×C₇×C₁₇	C₂×D₃	1	1	yes	characteristic, complemented
15	C₃×C₇×C₁₇	C₂²×C₃	1	1	yes	characteristic, complemented
16	C₂×C₃²×C₁₇	D₇	1	1	yes	characteristic, complemented
17	C₃×D₃×C₁₇	—	7	2	no	—
18	C₂×C₃×D₂₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₇×C₁₇	C₃×D₃	1	1	yes	characteristic, complemented
20	D₇×C₁₇	—	3	2	no	—
21	C₂²×C₃×C₁₇	—	21	1	no	—
22	C₂×D₃×C₁₇	—	7	1	no	—
23	C₃²×C₁₇	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃²×C₇	C₂×C₁₇	1	1	yes	characteristic, complemented
25	C₃×D₂₁	C₂×C₁₇	1	2	yes	direct product factor
26	C₇×C₁₇	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
27	C₂×C₃×C₁₇	—	2	1	no	—
28	C₂×C₃×C₁₇	—	21	2	no	—
29	C₂×C₃×C₁₇	C₃×D₇	1	1	yes	characteristic, complemented
30	C₂×C₃×C₁₇	D₂₁	1	1	yes	characteristic, direct product factor
31	D₃×C₁₇	—	7	2	no	—
32	C₂×D₂₁	C₃×C₁₇	1	1	yes	characteristic, direct product factor
33	C₂×C₃×D₇	—	3	1	no	—
34	C₂²×C₁₇	—	21	1	no	Hall
35	C₃²×C₇	C₂²×C₁₇	1	1	yes	characteristic, complemented, Hall
36	C₃×C₁₇	—	2	1	no	—
37	C₃×C₁₇	C₂×C₃×D₇	1	1	yes	characteristic, complemented
38	C₃×C₁₇	C₂×D₂₁	1	1	yes	characteristic, direct product factor
39	C₂×C₃×C₇	—	2	1	no	—
40	C₂×C₃×C₇	D₃×C₁₇	1	1	yes	characteristic, complemented
41	C₂×C₃×C₇	C₂×C₃×C₁₇	1	1	yes	characteristic, complemented
42	D₂₁	C₂×C₃×C₁₇	1	2	yes	direct product factor
43	C₃×D₇	—	3	2	no	—
44	C₂×C₃×D₃	—	7	1	no	Hall
45	C₂×C₁₇	—	21	2	no	—
46	C₂×C₁₇	C₃×D₂₁	1	1	yes	characteristic, direct product factor
47	C₂×D₇	—	3	1	no	Hall
48	C₃×C₇	—	2	1	no	—
49	C₃×C₇	C₂×D₃×C₁₇	1	1	yes	characteristic, complemented
50	C₃×C₇	C₂²×C₃×C₁₇	1	1	yes	characteristic, complemented
51	C₂×C₃²	D₇×C₁₇	1	1	yes	characteristic, complemented
52	C₃×D₃	—	7	2	no	—
53	C₁₇	C₂×C₃×D₂₁	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₇	C₃×D₃×C₁₇	1	1	yes	characteristic, complemented
55	D₇	—	3	2	no	—
56	C₂²×C₃	—	21	1	no	—
57	C₂×D₃	—	7	1	no	—
58	C₃²	C₂×D₇×C₁₇	1	1	yes	characteristic, complemented, Sylow
59	C₇	C₂×C₃×D₃×C₁₇	1	1	yes	characteristic, complemented, Sylow
60	C₂×C₃	—	2	1	no	—
61	C₂×C₃	—	21	2	no	—
62	C₂×C₃	C₃×D₇×C₁₇	1	1	yes	characteristic, complemented
63	C₂×C₃	C₁₇×D₂₁	1	1	yes	characteristic, direct product factor
64	D₃	—	7	2	no	—
65	C₂²	—	21	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₇×C₁₇	1	1	yes	characteristic, complemented
68	C₃	C₂×C₁₇×D₂₁	1	1	yes	characteristic, direct product factor
69	C₂	—	21	2	no	—
70	C₂	C₃×C₁₇×D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂²×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₇×C₁₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₂×C₃×C₁₇

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₁₇×D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₇×C₁₇	C₂	semidirect
3. C₂×C₁₇×D₂₁	C₃	direct (N × H)
5. C₃²×C₇×C₁₇	C₂²	semidirect
7. C₂×C₃×C₇×C₁₇	D₃	semidirect
8. C₂×C₃×C₇×C₁₇	C₂×C₃	semidirect
9. C₁₇×D₂₁	C₂×C₃	direct (N × H)
14. C₃×C₇×C₁₇	C₂×D₃	semidirect
15. C₃×C₇×C₁₇	C₂²×C₃	semidirect
16. C₂×C₃²×C₁₇	D₇	semidirect
18. C₂×C₃×D₂₁	C₁₇	direct (N × H)
19. C₂×C₇×C₁₇	C₃×D₃	semidirect
23. C₃²×C₁₇	C₂×D₇	semidirect
24. C₂×C₃²×C₇	C₂×C₁₇	semidirect
25. C₃×D₂₁	C₂×C₁₇	direct (N × H)
26. C₇×C₁₇	C₂×C₃×D₃	semidirect
29. C₂×C₃×C₁₇	C₃×D₇	semidirect
30. C₂×C₃×C₁₇	D₂₁	direct (N × H)
32. C₂×D₂₁	C₃×C₁₇	direct (N × H)
35. C₃²×C₇	C₂²×C₁₇	semidirect
37. C₃×C₁₇	C₂×C₃×D₇	semidirect
38. C₃×C₁₇	C₂×D₂₁	direct (N × H)
40. C₂×C₃×C₇	D₃×C₁₇	semidirect
41. C₂×C₃×C₇	C₂×C₃×C₁₇	semidirect
42. D₂₁	C₂×C₃×C₁₇	direct (N × H)
46. C₂×C₁₇	C₃×D₂₁	direct (N × H)
49. C₃×C₇	C₂×D₃×C₁₇	semidirect
50. C₃×C₇	C₂²×C₃×C₁₇	semidirect
51. C₂×C₃²	D₇×C₁₇	semidirect
53. C₁₇	C₂×C₃×D₂₁	direct (N × H)
54. C₂×C₇	C₃×D₃×C₁₇	semidirect
58. C₃²	C₂×D₇×C₁₇	semidirect
59. C₇	C₂×C₃×D₃×C₁₇	semidirect
62. C₂×C₃	C₃×D₇×C₁₇	semidirect
63. C₂×C₃	C₁₇×D₂₁	direct (N × H)
67. C₃	C₂×C₃×D₇×C₁₇	semidirect
68. C₃	C₂×C₁₇×D₂₁	direct (N × H)
70. C₂	C₃×C₁₇×D₂₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₁₇×D₂₁	2
C₂×C₃²×C₇×C₁₇	2
C₂×C₁₇×D₂₁	3
C₂×C₃×D₇×C₁₇	3
C₂×C₃×D₃×C₁₇	7
C₂×C₃×D₂₁	17

Subgroups — C2×C3×C17×D21 #16862837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₁₇×D₂₁ #16862837